Details

sample190.0ms

Algorithm

intervals

Results

9.0ms	29×	body	2560	valid
8.0ms	182×	body	80	valid
3.0ms	15×	body	1280	valid
2.0ms	7×	body	5120	valid
2.0ms	11×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify191.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	12	324
1	19	219
2	27	219
3	35	219
4	42	219
5	44	219
done	44	219

prune58.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize22.0ms

Local error

Found 1 expressions with local error:

1.5b	(- (hypot re im) re)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

11.0ms

(- (hypot re im) re)

series226.0ms

Counts

1 → 3

Calls

1 calls:

226.0ms

(- (hypot re im) re)

simplify4.7s

Counts

31 → 31

Iterations

Useful iterations: 5 (2.4s)

Iter	Nodes	Cost
0	61	7960
1	130	6752
2	237	5030
3	619	5030
4	1349	4550
5	3569	4406
done	5115	4406

prune208.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 15.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (hypot re im) re))
0.5b	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
1.5b	(- (hypot re im) re)
1.5b	(- (hypot re im) re)

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
35×	`sqrt-prod`
27×	`add-cube-cbrt`
20×	`pow1`
18×	`prod-diff`
14×	`sqrt-div`
12×	`swap-sqr`
9×	`sqrt-pow1` `flip3--` `pow1/2` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l` `add-log-exp`
7×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-l/` `associate-r/`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 142

Calls

4 calls:

8.0ms	(sqrt (- (hypot re im) re))
48.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
10.0ms	(- (hypot re im) re)
10.0ms	(- (hypot re im) re)

series917.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(sqrt (- (hypot re im) re))
102.0ms	(* (sqrt (- (hypot re im) re)) (sqrt (- (hypot re im) re)))
87.0ms	(- (hypot re im) re)
531.0ms	(- (hypot re im) re)

simplify2.4s

Counts

154 → 154

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	152	41766
1	324	32050
2	701	28485
3	1745	28356
done	5000	27371

prune764.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 15.2b

localize31.0ms

Local error

Found 1 expressions with local error:

18.1b

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series200.0ms

Counts

1 → 3

Calls

1 calls:

200.0ms

(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify4.3s

Counts

13 → 13

Iterations

Useful iterations: 4 (617.0ms)

Iter	Nodes	Cost
0	28	3975
1	52	2558
2	135	2118
3	455	2118
4	1418	2038
5	4960	2038
done	5000	2038

prune103.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 15.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
0.5b	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
18.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
18.1b	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`fma-udef`
1×	`pow2` `rem-sqrt-square` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

2.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
20.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
1.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

series843.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re)))
185.0ms	(* (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))) (sqrt (fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))))
178.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))
209.0ms	(fma (sqrt (hypot re im)) (sqrt (hypot re im)) (- re))

simplify2.1s

Counts

98 → 98

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	93	31792
1	209	20247
2	462	16805
3	1517	16412
done	5000	16237

prune558.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 15.2b

regimes159.0ms

Accuracy

0% (0.2b remaining)

Error of 13.3b against oracle of 13.1b and baseline of 13.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	219
1	11	219
done	11	219

end0.0ms

sample2.0s

Algorithm

intervals

Results

849.0ms	658×	body	2560	valid
465.0ms	6018×	body	80	valid
230.0ms	319×	body	5120	valid
189.0ms	503×	body	1280	valid
64.0ms	270×	body	640	valid
26.0ms	148×	body	320	valid
10.0ms	84×	body	160	valid